Homotopical Algebra - Model Categories

This seminar will be an introduction to the theory of model categories. This theory establishes an axiomatic framework for homotopy theory which has been very successful in analyzing homotopical phenomena and generalizing the methods of homological algebra to more general (non-additive) categories. The classical homotopy theories of topological spaces and chain complexes fit nicely in this framework and provide some of the main examples. The theory also provides a general framework in which different homotopy theories can be compared. The seminar should be of interest to anyone interested in algebraic topology, homological algebra and/or applications of categorical methods to topology and algebra. The detailed schedule of the seminar will be discussed at the preliminary meeting (Fr 30.1 14-15 M006). Talks will be held in English or German. Prerequisites: Some knowledge of basic category theory will be assumed. Familiarity with algebraic topology and/or homological algebra will be very useful in order to fully appreciate the origin and the scope of the theory, but it is not, strictly speaking, essential. Main references: The original source is Quillen's seminal monograph "Homotopical Algebra". Our main reference for the seminar will be Hovey's book "Model Categories". The long articles of Dwyer-Spalinski "Homotopy theories and model categories" and Goerss-Schemmerhorn "Model Categories and Simplicial Methods" are highly recommended.